Tensor products and Whittaker vectors for quantum groups

摘要

We describe the action of the center of the quantum group U-q(g) on the tensor product V x L(lambda) of an infinite-dimensional representation V having an infinitesimal character chi(tau) and an irreducible finite-dimensional U-q(g) representation L(lambda) of highest weight lambda. We apply this result in order to describe the tensor product of a Whittaker module and a finite-dimensional simple module for the algebra Uq(sl(2)).